Question: Solve for $x$ and $y$ using elimination. ${3x+y = 25}$ ${2x-y = 15}$
We can eliminate $y$ by adding the equations together when the $y$ coefficients have opposite signs. Add the equations together. Notice that the terms $y$ and $-y$ cancel out. $5x = 40$ $\dfrac{5x}{{5}} = \dfrac{40}{{5}}$ ${x = 8}$ Now that you know ${x = 8}$ , plug it back into $\thinspace {3x+y = 25}\thinspace$ to find $y$ ${3}{(8)}{ + y = 25}$ $24+y = 25$ $24{-24} + y = 25{-24}$ ${y = 1}$ You can also plug ${x = 8}$ into $\thinspace {2x-y = 15}\thinspace$ and get the same answer for $y$ : ${2}{(8)}{ - y = 15}$ ${y = 1}$